Notes

Casino Math

Craps

The key to understanding the mathematics of craps is to understand the dice combinations, or probabilities. We only want to make the most likely bets. These are the pass lines with odds, the come bets, the occasional place bets, the 6 and 8 don't pass placing the odds and can't be placed with or without the odds.

The house percentage in craps has the lowest rate of any casino game if you place the above-mentioned bets. Take single odds on come and pass lines reduces the house percent to 0.8 %... double and further reduces it to 0.06 Triple odds. Further, it drops to 0.0.5 quad odds which reduces it further to 0.0.5 %.... The game is almost even if you take 10 to 100 odds.

At games news , I am always asked why place bets are not as good as come bets. The answer lies with the combinations of dice. This can be illustrated with a place bet. A bet placed directly on the number 5, as an example (aka place bet), can only win on a total of four dice combinations: 1-4, 4-1, 2-3, 3-2. That's it! The bet loses when a 7 (which has 6 different combinations) is rolled. That's 6 to 4, or 3 to 2 against you based on the dice combinations alone.

Let's take a look at a "come bet". The come bet wins on a seven- or eleven-dice combination and loses on a 2, 3, or 12 for a total total of four dice combinations. more here 's 6-4, or 2 to 1 in favor of you for the immediate win over an immediate loss. If that come bet should go to the 5, as an example, it now has another 4 dice combinations to win. So, the come bet that started in the come area and went to the 5 had 12 dice combinations to win, versus only 5 combinations for the place bet on the 5. This is a significant advantage. This analysis can be used for any place bet.

When you consider that all come bets can be placed, the casino advantage is 6.7% for place wagers on the 4-10; 4% for place wagers on 5-9; 1.5% place bets upon the 6-8 and 8. A come wager, regardless of the number, is 0.8% with single chances and the exact opposite odds to the pass line.

To win at craps you need to minimize the casino's advantage. You also need to manage money so that you can capitalize on any streaks. The Benson Strategies help you do just that.

Blackjack

Blackjack is one of the few casino games where the advantage or disadvantage of the player changes with each card. laptop favors 4% the house, because if the dealer breaks, guess who takes the money. The house, of course!

Basic strategy can reduce the house advantage to 1.5%. This in itself makes it a good game to play. It is possible to expect a positive return with good basic play and smart money management.

In addition, basic strategy combined with tracking of cards played can increase the player's advantage by 1%. As long as there are no high cards in the deck or shoe, the player has an advantage. High cards favor the player because they give the player a better chance to get a "pat" hand and also they increase the dealer's chance of breaking. The dealer can only hit on 16 or fewer cards. The dealer will break more often if there is a high number of cards.

Simple hi-lo counts are good for single deck games, and card clumping is good for shoe games. These are the most common methods of tracking. If blackjack is played well, it offers a 1% mathematical advantage.

Baccarat


Baccarat, like craps, roulette, or other casino games, is known for having a negative expectation. This means that the house is always in the lead. This means that mathematically, there is no way to place the odds in the favor of the player. This is possible only with perfect blackjack card counting (which, of course, doesn't let them let you win much).

The way we win at baccarat is to follow the trend. A trend will develop in any random or near random series of events. It is important to remember that you won't have enough data to make statistically significant probabilities. These numbers are dependent on a lot more play. One possibility is that there are 50% more bankers than players, which would be very interesting.

zoom games to play sees real statistical significance since they have so much action going on all the time. They cannot lose from gaming itself. They will only lose if they don't get enough players, or in typical business profit/loss scenarios. However, they can't lose on the gaming. This is impossible. But it is very possible for the casino to lose to individual players. These losses are compensated by the casino because they have enough players who can make the math work for them long-term.

This last point should be very important. Because unless you play 24 hours a day, you will never be playing by the same mathematical statistics as the casino. Our money management and departure rules eliminate this instantly. A bad play and/or lack of discipline will not win the Baccarat player.

Roulette

Roulette has an advantage of 5.26% over the player. This is because of the 38 numbers that are on the wheel: 1-36, zero and 00. However, the payoffs are only based on the 36 numbers and not the 0 or 00. 35-1 is the single number. So, simply stated, the 0 and 00 are the casino's edge.

Over a long period, the casino will have an definite mathematical advantage.

Casino's Math

Needs lots of playing action to achieve true odds.
All statistics are based on an infinite number of rolls.
Variations in bet sizes are known as Hates deviations.
Structured play is not for him, particularly in the area of money management and departure rules.
Once the volume of play is achieved the mathematical edge is guaranteed.
The casino will offer any enticement to achieve this guaranteed mathematical edge.




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